Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian

Details Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian

2012-02-02

arxiv.org/abs/1202.0576v1

Mathematics

Analysis of PDEs

Scientific paper

This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

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